Terry Ryan said it at least three times during Ron Gardenhire’s rehiring news conference Monday: Starting pitching is his top priority this offseason. “There were too many nights where our starting pitcher didn’t give us a chance to win,” Ryan said of his rotation, which pitched the fewest innings and owned the worst ERA in the majors. “We need to start with the starting pitching and go from there.”

Of course, acquiring starting pitching was his chief objective last winter, too, but his most notable acquisitions — minor league prospects Trevor May and Alex Meyer — are still a year or two away from the majors. This season, the need is more immediate.

Trades such as last winter’s, where the Twins dealt away outfielders Denard Span and Ben Revere, are a possibility, particularly given Ryan’s assertion that he is willing to consider anything. But the combination of Ryan’s stated mission, and owner Jim Pohlad’s blessing to increase the team’s roughly $80 million payroll, likely means the Twins will be bidding on free agents, perhaps more than ever before.

“We probably have to go out to the market to supplement the roster for 2014,” Pohlad said, “[and] I think [Ryan] is enthusiastic about doing that.”

So what’s he going to find when he starts shopping? Here’s a guide to a handful of the Twins’ most logical targets, some more likely than others:

Mike Pelfrey: By objective standards, his first season with the Twins was disappointing, with a 5.19 ERA, a high walk rate and way too many baserunners. But Pelfrey and the Twins both seem relatively encouraged, considering he made 29 starts despite coming off elbow surgery in May 2012, and both sides appear interested in keeping him here. His agent, Scott Boras, will be shopping for a multiyear contract and a raise from his $4 million salary, making him a relatively big gamble.

Scott Kazmir: No team figures to be more impressed with the two-time All-Star’s comeback than the Twins, who faced the Cleveland lefthander five times and scored only five earned runs. Kazmir wasn’t really that unhittable, but he’s still interesting: lefthanded, only 30 next year, and showing the best control of his career. Like Pelfrey, he’s a risk, but he throws hard and probably will be in the Twins’ price range.

Matt Garza: The former Twins righthander figures to be the priciest free-agent pitcher on the market this year, despite a subpar couple of months in Texas after he was traded from the Cubs. His strikeout rate has begun to decline, making it questionable whether he can be a No. 1 starter again.

Jason Vargas: A lefty who fits the Twins’ put-it-in-play mold, with a fastball that barely reaches 90 miles per hour. His season with the Angels was marred by a blood clot that required surgery, but he still pitched 150 innings with a 4.02 ERA. His problems with home runs would be helped by pitching at Target Field.

Scott Feldman: Four years removed from a 17-win season with Texas, he will be 31 and owns a 4.13 ERA over the past three seasons with fewer than one homer per nine innings, despite playing in home-run bandboxes for the Rangers, Cubs and Orioles, his team in 2013. A reliable league-average No. 3 or 4 starter.

Phil Hughes: The Twins discussed acquiring him during the Johan Santana talks six years ago, but he never lived up to his first-round promise with the Yankees, posting ERAs above 5.00 two of the past three years. Still, he is only 27, and he is a significantly better pitcher (4.10 career ERA) away from Yankee Stadium.

Joba Chamberlain: Another Yankees disappointment, this is an outside-the-box possibility that might be worth considering, for both sides. He is only 28, and like Hughes, the Nebraska native might also fare better outside New York. It’s a large risk, since the Yankees stuck him in the bullpen, where he has averaged only 40 innings for four years. But his ERA was 4.18 as a starter, with a high strikeout rate (and walk rate, too).

Ervin Santana: Still only 30, he posted a 3.24 ERA for the Royals in 211 innings, a high point in an up-and-down career. He is homer-prone, but again, Target Field would help with that. He earned $13 million this season and will be looking for a raise, so it would require a non-Twins-like commitment.

Masahiro Tanaka: He went 20-0 in Japan’s Pacific League with a 1.24 ERA this year, and he will be 25 next season. Interested? Yeah, so are the other 29 big-league teams. This one would take a huge commitment from the Twins, whose previous foray into Japanese baseball, Tsuyoshi Nishioka, didn’t go so well. Tanaka doesn’t have the raw stuff of Yu Darvish, but he is a polished pitcher who doesn’t walk many and keeps the ball in the park. The posting fee required to win the rights to talk to Tanaka probably won’t reach Darvish’s $51 million heights, but there’s no doubt he would require the biggest free-agent commitment in Twins history.